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I'm sure there is a shorter, more formal way to do this, but here you go. "S" is the small number, "L" is the larger.

Two equations given:

1) L=S+6

2) S+3xL=34

Using equation #1, substitute (S+6) for L in Equation #2:

S+3x(S+6)=34

Convert 3x(S+6) to 3xS + 3x6:

S+3xS+3x6=34

3x6=18:

4xS+18=34

Subtract 18 from both sides of the equation:

4xS=16

Divide both sides of the equation by 4:

S=4

If S=4, and L=S+6, then L must be 10:

Plug the numbers back into equation #2 to test it:

4+(3x10)=34

Jim

phranque, i am Russian, i do it in my head :),i had 5+ in math

when a 5th grader asks for help in math, the worst thing you can do is give him/her the answer (only).

Let me guess, PHP, SQL & Basic pro or just good at maths?!

no php, plenty of sql, no basic of any flavor for decades, plenty of math way back when, kids in school...

Surely this is much simpler as you know that one number is 6 less than the higher number you can look for 4 times the higher number knowing without worrying about the lower number until you have the first answer (no need to overcomplicate the logic on this one):

3x + (x - 6) = 34

>> Which simplifies to

4x - 6 = 34

>> move the 6 over (changing the sign)

4x = 34 + 6

>> Add

4x = 40

>> Dividing gives

x = 10

>> Find smaller number

y = x - 6

>> which gives

y = 4

>> Hence (after checking 3*10 + 1*4 = 34)

Larger number = 10

Smaller number = 4

I agree that it's not good to give a 5th grader the answer to an algebra problem, in addition I don't think you should give them the method. Teaching methods is what the school has done, the homework is evidently designed to stretch the 5th grader's ability to reformulate the problem intuitively. More time (as long as it takes), a mug of coffee, and a room with no distractions are the best way for a student to solve a mathematics problem.

In the UK we have a TV program called 'Are You Smarter than a 10 Year Old'. While I'm not sure how old a 5th grader is, older than that by the looks of the question, I'm regularly astounded at some people's lack of knowledge of anything.

One question an adult couldn't answer:

Some bloke works for 10 hours, and sleeps for 8. In it's simplest form, what fraction of the day does he work?

Another:

What is the young of a Kangaroo called?

I can't believe people don't know this stuff!

One question an adult couldn't answer:

Some bloke works for 10 hours, and sleeps for 8. In it's simplest form, what fraction of the day does he work?Another:

What is the young of a Kangaroo called?

Not being able to perform (fairly) basic math is one problem, not being able to recall (or never having learned) a bit of trivia that isn't critical in real life (unless you're on Jeopardy and that's the question for Final Jeopardy) is another story.

On the other hand, if you lived in Australia and couldn't answer the 2nd question...

[**edited by**: LifeinAsia at 5:02 pm (utc) on Nov. 21, 2007]

algebra isn't usually taught in 5th grade - that must be some school

We got a recommendation spit out by a computer from school that we work on Geometry with our 5th grader. Okeedoke.

And yes, some of the homework my 5th grade has been bringing home looks a lot like Algebra. I think it's supposed to be "guess and check" but some of the kids are using variable substitution because it's quicker.

Dabu The Dragon, I assume you're not a programmer? In my opinion, the best way to learn algebra for a kid is to learn to write programmes. Nowhere else will constantly be challenged to write and solve equations of all levels of complexity whilst thoroughly enjoying themselves.

Pick a comprehensive but syntactically simple language such as a BASIC derivative and teach the kid how to build simple apps, games, toys etc. As a childhood hobby it is very engaging and involving and has the side effects of high intellectual stimulation at very minimal ongoing investment compared to most hobbies.

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